APPENDIX: POTENTIAL, FIELD AND RADIATED MOMENTUM OF AN ACCELERATED POINT-LIKE MAGNETIC DIPOLE MOMENT

Even though the focus of this article is on the T.E. radiation from an axially symmetric circular dipole antenna, the mathematical structure of T.M. radiation is virtually the same for both. One merely has to interchange the magnetic with the electric field components to obtain one from the other. Furthermore, both are derived from a single scalar which obeys the same inhomogeneous scalar wave Eq.(5). For T.E. radiation from a magnetic dipole localized at $r'=0$ and $\xi'=constant$ in Rindler sector $I$ (upper sign) or $II$ (lower sign), this scalar is the simplified version of Eq.(61):

$$\psi_F(\xi,\tau,r,\theta)=\frac{2\pi a^2}{2\xi\xi'} \frac{\pm 1}{\sqrt{u^2+1}} \frac{dq(\tau \pm \sinh^{-1}u)}{d\tau}$$ (78)

where

$$u =\frac{\xi^2-\xi^{'2} -r^2}{2\xi \xi'}$$

What are the T.E. field components and what is the Poynting integral, Eq.(65)? With some care the calculation is reasonably straight forward. We exhibit the calculational path in this appendix because it probably is optimal and hence also useful for the case of T.M. radiation.